Recognising Algebraic Surfaces from Two Outlines

  • Simon Collings
  • Ryszard Kozera
  • Lyle Noakes


Photographic outlines of 3 dimensional solids are robust and rich in information useful for surface reconstruction. This paper studies algebraic surfaces viewed from 2 cameras with known intrinsic and extrinsic parameters. It has been known for some time that for a degree d=2 (quadric) algebraic surface there is a 1-parameter family of surfaces that reproduce the outlines. When the algebraic surface has degree d>2, we prove a new result: that with known camera geometry it is possible to completely reconstruct an algebraic surface from 2 outlines i.e. the coefficients of its defining polynomial can be determined in a known coordinate frame. The proof exploits the existence of frontier points, which are calculable from the outlines. Examples and experiments are presented to demonstrate the theory and possible applications.


Computer vision Algebraic surfaces Outlines Stereo 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of Western AustraliaPerthAustralia
  2. 2.School of Computer Sience and Software EngineeringUniversity of Western AustraliaPerthAustralia

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